Systems and methods for positioning and measuring objects using a cmm

ABSTRACT

Objects having complex geometries, such as tubular segments with multiple bends, can be measured using a system including a coordinate measurement machine. The system can include multiple supports for the object to reduce error due to sag of an object under its own weight. The supports can include positionable support members formed of metal tape. The system can further include a processor configured to determine one or more support locations for the object based on a set of definition data for the object. With support locations for the object have been determined and supports placed, the object can be measured, and a post-comparison operation can be performed. Where the object differs greatly from the definition data, the support locations can be revised.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 60/800,336, entitled “SYSTEMS AND METHODS FORPOSITIONING AND MEASURING OBJECTS USING A CMM,” filed on May 15, 2006.

Also, this application hereby incorporates by reference theabove-identified provisional application, in its entirety.

LIMITED COPYRIGHT AUTHORIZATION

A portion of the disclosure of this patent document contains materialwhich is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightrights whatsoever.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present disclosure generally relates to articulated arm coordinatemeasuring machines, and in particular, to systems and methods forpositioning objects for measurements with coordinate measuring machines.

2. Description of the Related Art

Various objects, including tubular objects having multiple bends, can bemeasured with coordinate measuring machines. Tubular objects havingmultiple bends can be supported by a clamp near the center of gravity ofthe object while measurements are made.

SUMMARY OF THE INVENTION

One embodiment of the present teachings relates to a system forproviding support for an object to be measured by an articulator. Thesystem includes a definition data. The system further includes acontroller configured so as to determine one or more support locationsfor the object based on the definition data.

In one embodiment, the one or more support locations are determinedbased on determination of a selected desired orientation and position ofthe object. In one embodiment, the orientation and position aredetermined based on a selected preferred range of motion for thearticulator.

In one embodiment, the system further includes one or more supportmembers that can be moved to the support locations to provide thesupport for the object. In one embodiment, the one or more supportmembers are moved by the articulator based on known starting locationsof the one or more support members and the one or more supportlocations. In one embodiment, the one or more support members are movedmanually to the one or more support locations, with the movementsfacilitated by the articulator being positioned at the one or moresupport locations.

In one embodiment, each of the one or more support members includes abase that allows lateral movement or the support member, and aretractable member that provides adjustable height for the supportlocation corresponding to the support member. In one embodiment, theretractable member includes a retractable tape.

In one embodiment, the support member further includes a blocking memberthat inhibits downward movement of the retractable member. In oneembodiment, the blocking member is actuated by the articulator. In oneembodiment, the support member further includes a stability enhancingmember that selectively provides additional stability of the supportmember.

In one embodiment, the system further includes a return facilitatingmember disposed on the support member and a nesting assembly configuredto receive the return facilitating member.

In one embodiment, the controller is further configured so as to obtainmeasurements of the object by movements of the articulator, where thearticulator movements are based on the definition data. In oneembodiment, the controller is further configured so as to compare theobject measurements with the definition data. In one embodiment, thecontroller is further configured so as to perform a post-comparisonoperation. In one embodiment, the post-comparison operation includesidentifying of differences between the object measurements and thedefinition data. In one embodiment, the post-comparison operationincludes marking of the object based on the comparison. In oneembodiment, the controller is further configured so as to adjust thearticulator movements to account for deviations of the object from thedefinition data.

One embodiment of the present disclosure relates to a method forproviding support for an object to be measured by an articulator. Themethod includes obtaining a definition data. The method further includesdetermine one or more support locations for the object based on thedefinition data.

In one embodiment, the one or more support locations are determinedbased on determination of a selected desired orientation and position ofthe object. In one embodiment, the orientation and position aredetermined based on a selected preferred range of motion for thearticulator.

In one embodiment, the method further includes generating signals forthe articulator, the signals resulting in movements of one or moresupport members to the support locations to provide the support for theobject. In one embodiment, the one or more support members are moved bythe articulator based on known starting locations of the one or moresupport members and the one or more support locations. In oneembodiment, the one or more support members are moved manually to theone or more support locations, with the movements facilitated by thearticulator being positioned at the one or more support locations.

In one embodiment, the method further includes obtaining measurements ofthe object by movements of the articulator, where the articulatormovements are based on the definition data. In one embodiment, themethod further includes comparing the object measurements with thedefinition data. In one embodiment, the method further includesperforming a post-comparison operation. In one embodiment, thepost-comparison operation includes identifying of differences betweenthe object measurements and the definition data. In one embodiment, thepost-comparison operation includes marking of the object based on thecomparison. In one embodiment, the method further includes adjusting thearticulator movements to account for deviations of the object from thedefinition data.

One embodiment of the present disclosure relates to a system foroperating an articulator. The system includes means for obtainingdefinition data. The system further includes means for determining oneor more support locations for an object to be measured by thearticulator based on the definition data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of one embodiment of a control system foran articulator;

FIG. 2 shows one embodiment of a process that can be performed by thecontrol system to determine one or more support locations for supportingan object based on a definition data of the object;

FIG. 3 shows one embodiment of a process that can be performed by thecontrol system once the object is supported at the support locationsdetermined by the process of FIG. 2;

FIGS. 4A and 4B show that in one embodiment, the control system cangenerate signals that result in the articulator positioning supportmembers at the support locations;

FIGS. 5A and 5B show that in one embodiment, the control system cangenerate signals that result in the articulator aiding in manualpositioning of support members at the support locations;

FIG. 6 shows an example comparison of an example object with a depictionof the object's corresponding definition data, showing that similarcomparison can be made by the process of FIG. 3;

FIG. 7 shows that in a conventional supporting technique, one or moreportions of the supported object can flex or sag, thereby resulting inan inaccurate comparison with the definition data;

FIG. 8 shows an example of one embodiment of a supporting technique,where the object is supported at a plurality of selected locations thatreduce the unwanted flexing of sagging of the object, and where suchlocations can be selected to facilitate measurement of the supportedobject;

FIG. 9 shows an example where the articulator under the control of thecontroller has positioned the support members so as to allow positioningof the object thereon;

FIG. 10 shows an example definition data corresponding to the exampleobject of FIG. 9, where the definition data is shown to be input intothe controller;

FIG. 11 shows an isolated view of a depiction of the definition data ofFIG. 10;

FIG. 12 shows an example of how the definition data can be used todetermine the support locations so that the object supported thereon canbe oriented in a selected orientation with respect to the articulator;

FIG. 13 shows an example of how the definition data can be used todetermine the support locations so that the object supported thereon canbe positioned in a selected location with respect to the articulator anda support surface;

FIG. 14 shows an example of how the definition data can be used todetermine selected support locations that facilitates measurement of theobject supported thereon;

FIG. 15 shows one embodiment of a process that can determine the exampleselected orientation of FIG. 12;

FIG. 16 shows one embodiment of a process that can determine theselected location of FIG. 13;

FIG. 17 shows one embodiment of a process that can determine theselected support locations of FIG. 14;

FIG. 18 shows one embodiment of a process that generates signals to movea plurality of support members from known storage locations to theselected support locations;

FIG. 19 shows an example movement of the support members of FIG. 18;

FIG. 20 shows an example process for positioning of three examplesupport member and measuring of the example object of FIG. 11;

FIG. 21 shows one embodiment of a process that compares the measurementof the object with the definition data and performs a post-comparisonoperation;

FIG. 22 shows one embodiment of a process that performs an examplepost-comparison operation where marks are made at locations for cuttingoff of end tabs that were used for manufacturing and handling;

FIG. 23A shows one embodiment of an example support member in its storedconfiguration;

FIG. 23B shows the example support member of FIG. 23A in its deployedconfiguration so as to provide a support for the object being measured;

FIG. 24 shows a cut-away depiction of one embodiment of the supportmember;

FIGS. 25A and 25B show cut-away depictions of another embodiment of thesupport member;

FIGS. 26A and 26B show that in one embodiment, the support member caninclude a storage nest indexing member that allows for accuratepositioning of the support member when stored, and/or a stability memberthat provides additional stability when the support member is in itsdeployed configuration;

FIG. 27A shows an example situation where the object being measured canbe deviate significantly from the definition data, and where the supportlocations can be adjusted based on such deviation to facilitatemeasurements of the object;

FIG. 27B shows an example situation where the object being measured canbe deviate significantly from the object data, such that if thearticulator moves according to the definition data, it can eithercontact the object and/or miss the object;

FIG. 28 shows one embodiment of a process that can perform a correctiveaction to account for deviations such as those of FIGS. 27A and 27B;

FIG. 29 shows one embodiment of a process that can adjust supportlocations to account for the example situation of FIG. 27A;

FIG. 30 shows one embodiment of a process that can adjust measurementmovements to accommodate the example situation of FIG. 27B; and

FIG. 31 shows one embodiment of an example of the process of FIG. 30.

These and other aspects, advantages, and novel features of the presentdisclosure will become apparent upon reading the following detaileddescription and upon reference to the accompanying drawings. In thedrawings, similar elements have similar reference numerals.

DETAILED DESCRIPTION OF SOME EMBODIMENTS

The present teachings generally relate to systems and methods forpositioning objects for measurements with articulators. In thedescription herein, an articulator may also be referred to as a CMM(coordinate measuring machine).

FIG. 1 shows a block diagram of one embodiment of a controller 100 thatcan receive definition data 104 and generate output signals 106 thatresult in movements of an articulator. As described herein, suchmovements can either position one or more support members at selectedlocations, or facilitate such positioning of the support members.

In one embodiment, the definition data 104 can be input to thecontroller 100, obtained from a database, or any combination thereof. Inone embodiment, the controller 100 includes a processor 102 that can beconfigured so as to generate the output signals 106 based on thedefinition data 104. Examples of the definition data and datacorresponding to the output signals are described below in greaterdetail.

In one embodiment, the controller 100 can also be configured to receivemeasurement signals 108 from the articulator. As described herein, theoutput signals 106 can facilitate positioning of an object formeasurement based on the corresponding definition data 104. Once theobject is positioned, the articulator under the control of thecontroller 100 can measure the object to yield the measurement signals108. Such measurement of the object can be compared to the definitiondata 104. As described herein, such comparison can be used as a qualitycontrol technique where the actual dimensions of the object (that wasfabricated based on the definition data) is compared to the “ideal”dimensions defined in the definition data. For such comparison, as onecan appreciate, it is desirable to have the object positioned in astable and consistent manner for measurement. Various features of thepresent disclosure facilitate such positioning and measurement of theobject to be measured.

For the purpose of description herein, the processor 102 can include oneor more processing devices. Thus, for example, the generation of theoutput 106 and the analysis of the measurement signals can be performedby one processing device or a plurality of separate processing devices.Similarly, the controller 100 can include one or more devices, and/orone or more processes, and/or any combination thereof.

In general, it will be appreciated that the processors can include, byway of example, computers, program logic, or other substrateconfigurations representing data and instructions, which operate asdescribed herein. In other embodiments, the processors can includecontroller circuitry, processor circuitry, processors, general purposesingle-chip or multi-chip microprocessors, digital signal processors,embedded microprocessors, microcontrollers and the like.

Furthermore, it will be appreciated that in one embodiment, the programlogic may advantageously be implemented as one or more components. Thecomponents may advantageously be configured to execute on one or moreprocessors. The components include, but are not limited to, software orhardware components, modules such as software modules, object-orientedsoftware components, class components and task components, processesmethods, functions, attributes, procedures, subroutines, segments ofprogram code, drivers, firmware, microcode, circuitry, data, databases,data structures, tables, arrays, and variables.

FIG. 2 shows one embodiment of a process 110 that can be performed bythe processor 102 of FIG. 1 to generate the output signals 106 for thearticulator. In a process block 112, definition data for an object isobtained. In a process block 114, one or more support locations forsupporting an actual object are determined based on the definition data.In a process block 116, one or more signals are generated to yieldmovement(s) of an articulator to facilitate positioning of one or moresupport members to support the actual object at the one or more supportlocations.

FIG. 3 shows one embodiment of a process 120 that can be performed bythe processor 102 of FIG. 1 for processing of the measurement signals108 from the articulator. In a process block 122, measurement of anactual object is obtained. In a process block 124, the actual objectmeasurement is compared with a definition data representative of theobject. In a process block 126, one or more operations can be performedbased on the comparison. Examples of such post-comparison operations aredescribed below in greater detail.

FIGS. 4A and 4B show that in one embodiment, an articulator 130 can bemoved (due to the output signals 106 of FIG. 1, and the process block116 of FIG. 2) so as to move a plurality of support members 132 toselected locations. FIG. 4A shows that the support member 132 a has beenmoved (depicted by an arrow 134) from its “nest” (a storage location)136 a to its selected location by the articulator 130. Other supportmembers 132 b and 132 c, in their respective nests 136 b and 136 c, canalso be moved to their respective selected locations in a similarmanner.

FIG. 4B shows that in one embodiment, the support member 132 can includea height-adjustable member 140 whose height is being adjusted (depictedby an arrow 142) by the articulator 130. If the top portion of themember 140 is to provide support for the object (not shown), the member140 can be raised or lowered so as to place the top portion at thesupport location.

In one embodiment, the example movement 134 and the exampleraising/lowering movement 142 can be performed in any order. Asdescribed herein, such example movements of the articulator 130(resulting in the movements 134 and 142 of the support member 132 andthe height-adjustable member 140) can result from the output signals 106generated by the controller 100.

In one embodiment, the articulator can be moved not to move the supportmember, but to facilitate accurate positioning of the support member atthe support location. Thus, in FIGS. 5A and 5B, the articulator 130 isdepicted as being positioned at a location so as to provide an index forpositioning of the support member 132 (FIG. 5A) and for heightadjustment of the member 140 (FIG. 5B). In one embodiment, the foregoingpositioning and height adjustment can be performed manually.

In some embodiments, positioning and height adjustment movements can beachieved by the articulator (as in FIG. 5A). In other embodiments,positioning and height adjustment movements can be achieved manually (asin FIG. 5B). In other embodiments, positioning and height adjustmentmovements can be achieved by a combination thereof.

FIG. 6 shows an example object 152 that was fabricated based on adefinition data that is represented as a dashed-line object 150. As thecomparison shows, the fabricated object 152 may have variations (forexample, at the right end) from the definition data. Such variations canresult from, for example, fabrication errors, and can be detected bycomparison of the object 152 measurements with the definition data 150.

As further shown in FIG. 6, some fabricated objects can include portionsthat aid in the fabrication, but are later removed. For example, theobject 152 is shown to have end tabs 154 that extend beyond the definedends of the definition data 150. Such end tabs 154 can aid infabrication and handling of the object 152, and removal of such tabs canbe facilitated by the articulator as described below in greater detail.

It will be understood that the definition data 150 shown in FIG. 6 isnot a physical object, but rather a depiction of some data. Thus, such“virtual” object (at least to the extent used for dimensionaldefinition) does not necessarily manifest mechanical properties, and isnot necessarily affected by forces due to, for example, support andgravity. However, the actual object 152 can manifest mechanicalproperties, and can be affected by forces due to support and gravity.

FIG. 7 shows an example of a prior art support member 160 supporting theobject 152 at a single location. Typically, such support member 160clamps the object 152 near the object's center of gravity, after whichmeasurements can be made with the articulator. With such a support,however, the ends of the object 152 can sag due to gravity or besusceptible to flexing motion (depicted as arrows 162). Such saggingand/or flexing motion can be significant especially if the object 152 isrelatively long.

FIG. 8 shows that by providing a plurality of supports 170 at locationsdistributed along the object 152, such sagging and/or flexing can bereduced. As described herein, various features of the present disclosurecan determine locations of such support locations so as to position theobject 152 in some selected location and orientation for measurementswith the articulator. It will be understood that, although threesupports are shown as an example, other numbers of supports can be used.Moreover, although multiple supports may be preferable, some features ofthe present disclosure do not necessarily need to have such multiplesupports.

FIG. 9 shows a photograph of an example setup 180 where an exampleobject 182 is shown to be supported by three example support members 184a, 184 b, and 184 c. The support members 184 a, 184 b, and 184 c areshown to respectively provide support locations 186 a, 186 b, and 186 cfor the object 182. As described below in greater detail, the supportlocations 186 a, 186 b, and 186 c are provided by movements of thearticulator 130 under the control of the controller 100.

In FIG. 9, a marker holder 190 is also shown. The holder 190 can beconfigured to hold a marker and be positioned at some known location.The articulator can be instructed to pick up and move the marker andmark the object (to indicate locations for cutting off of the end tabs,for example) in a manner describe below in greater detail.

For the purpose of description, an example coordinate (x,y,z) system 192can be defined where the X-Y plane is defined by the table-top 194, andthe origin is at the rotational axis of the base member of thearticulator 130. For the shown X and Y axes, the positive Z axis pointsupward. Other coordinate definitions are possible.

As described above, the controller 100 can receive a definition data soas to generate articulator-movement signals and/or to compare with thearticulator measurements of the object. FIG. 10 shows an exampledefinition data 200 for the example object 182 shown in FIG. 9. As shownin FIG. 9, the example object 182 has six sections joined by bends. Oneway to define such an object is to define coordinate values for the twoends (of the object) and the five intersection points for the sixsections (assuming that the sections extend straight past theirrespective bends). Thus, the seven rows of “mxyz” numbers indicate the(x,y,z) coordinates of the two ends and the five intersection points andthe radius of curvature of the bends. For the particular example object182, all of the bends (“PRBR”) are defined to be approximately 38.10 mm.

If an object is a tubular shaped object, the definition data can alsodefine the outer diameter and the inner diameter. For this particularexample, the object 182 is a solid rod; thus, both outer (“AEDI”) andinner (“BEDI”) diameters are shown to be defined as being approximately12.70 mm.

FIG. 11 shows an isolated view of a “virtual” object 210 as defined bythe example definition data 200 of FIG. 10. As shown, the six sectionsare indicated as 212 a-f; the five bends are indicated as 214 a-e; andthe two object-ends are indicated as 216 a and 216 b. For the purpose ofdescription herein, the two object-ends 216 a and 216 b, andintersection points corresponding to the bends 214 a-e, are referred toas definition points for the virtual object 210.

FIGS. 12 and 13 show how the definition data 200 can be used todetermine selected orientation and location of the object to besupported for measurement. FIG. 14 shows how a plurality of supportlocations can be determined to support the object in such orientationand location.

FIG. 12 shows an example of how the definition points 218 a-g can beused to determine a selected orientation of the virtual object 210, andthus the orientation of the actual object when positioned. In oneembodiment, the coordinates of the definition points 218 a-g can be fitwith a selected curve 220, where the selected curve 220 can representsome preferred range of motion of the articulator. For example, theselected curve 220 can be an arc that, along with a point 226 (along theZ-axis), define a plane 222. In one embodiment, the plane 222 issubstantially parallel with the table-top surface (194 in FIG. 9). Thearc 220 can be made to substantially coincide with a preferred motionarc 224 of the articulator. Fitting of the arc 220 (and thus thepreferred motion arc 224 of the articulator) to the definition points218 a-g can be achieved using any of a number of known techniques (forexample, least-square fit). By fitting the definition points 218 a-g inthe foregoing manner, an object oriented accordingly can be measured inan efficient manner, since the articulator would not have to deviatemuch from its preferred range of motion (for example, along the motionarc 224).

FIG. 13 shows the virtual object 210 when viewed in the plane 222 andtowards the point 226. The virtual object 210 is shown to be oriented inthe foregoing manner so that the definition points 218 a-g are generallylocated about the plane 222. In one embodiment, the height “h” of theplane 222 relative to the surface 194 (z=0) can be determined based onthe range of adjustable heights of the support members.

FIG. 14 shows that support locations 186 can be determined for an object(depicted as the virtual object 210) in different ways. In oneembodiment, a support location (186 b) can be provided at or near thecenter of gravity of the object. Support locations (186 a and 186 c) canalso be provided near the ends of the object so as to reduce orsubstantially eliminate the sagging or flexing effect. Additionalsupport locations can be provided as needed (for example, if the objectis longer and/or more flexible).

In one embodiment, as shown in FIG. 14, the support locations 186 can bedetermined so as to allow measurements of the object with supportspositioned at such locations. For example, in one set of measurements,each of the sections (depicted as 212 a-f) is measured at two points toprovide directionality. Projections based on the directionalities,combined with bend-radius information, allow reconstruction of themeasured object.

Thus, in such an example measurement scheme, it is not necessary tomeasure the bends. Accordingly, support locations can be provided atbends (for example, 186 a and 186 b are located at what would be bendsin the actual object). Since two points are measured for a givensection, it is also not necessary to measure the entire length of thatsection. Accordingly, a support location can be provided near a mid-waypoint of a section, so as to allow measurements at two points about thesupport location.

Different considerations can be taken into account to determine use ofthe foregoing example support locations. For example, if a given sectionis short, then it would not make sense to use the mid-section support.Also, the end sections (212 a and 212 f) may need to have their outerend points (218 a and 218 g in FIG. 13) measured. In such a situation,support should not be located at the outer end points. In FIG. 14, theexample supports 186 a and 186 c both allow measurements of the outerends.

FIGS. 15 and 16 show processes that can be performed by the controllerto effectuate the object orientation and location configurationsdescribed by way of examples in reference to FIGS. 12 and 13. FIG. 17shows a process that can be performed by the controller to effectuatethe support location configuration described by way of example inreference to FIG. 14.

FIG. 15 shows one embodiment of a process 240 that can be performed bythe controller. In a process block 242, selected points on a definitiondata object are obtained. For the example definition data object 210 ofFIG. 12, the selected points can be the definition points 218 a-g. In aprocess block 244, a selected curve is fit for the selected points. Inone embodiment, an arc is fit for the selected points. In a processblock 246, the definition data object is oriented so that the fit curvesubstantially coincides with a selected articulator movement curve. Inone embodiment, the fit arc substantially coincides with a preferredmovement arc of the articulator.

FIG. 16 shows one embodiment of a process 250 that can be performed bythe controller. In a process block 252, a desired orientation of adefinition data object is obtained. In one embodiment, process 240 ofFIG. 15 can provide such desired orientation. In a process block 254, adesired height of the definition data object in the desired orientationis obtained.

FIG. 17 shows one embodiment of a process 260 that can be performed bythe controller. In a process block 262, desired orientation and locationof a definition data object are obtained. In one embodiment, processes240 and 250 of FIGS. 15 and 16 can provide a desired orientation and adesired height, respectively. In a process block 264, a plurality ofsupport locations are determined based on the definition data object.

FIG. 18 shows one embodiment of a process 270 that can be performed bythe controller to facilitate positioning of support members according tosupport-locations determination. In a process block 272, a plurality ofsupport locations for supporting an object are determined. In oneembodiment, such support locations can be determined via the processes240, 250, and 260 described above in reference to FIGS. 15-17. In aprocess block 272, signals are generated for movements of thearticulator to move a plurality of support members from known locationsto the support locations.

FIG. 19 shows an example situation 280 where support members 184 a, 184b, 184 c, 184 d are in the process of being moved from known locations(for example, at nests 282 a, 282 b, 282 c, 282 d) to support locations.In FIG. 19, the definition data (virtual) object 210 is shown for visualreference; however, it does not exist physically.

In the example shown in FIG. 19, the first example support member 184 ais depicted as being already positioned at the first support location(depicted as 186 a). The articulator 130 is in the process of moving thesecond support member 184 b from the second nest 282 b to its supportlocation. The third support member 184 c is depicted as still being atthe third nest 282 c. In one embodiment, additional support member(s)(depicted as 184 d) may be present for supporting other types of objectsand/or other support configurations.

FIG. 20 shows one embodiment of a specific example process 290 that canbe performed to position the three example support members at theirsupport locations, and to perform measurements of an actual objectsupported thereon. The object supported at the support locations by thesupport members is generally depicted in FIG. 9. In the process 290,various “Step” data are referred to. Examples of such “Step” data arelisted at the end of this section (“DESCRIPTION OF SOME EMBODIMENTS”).It is understood herein that although sequentially numbered, the Stepsdescribed with reference to FIG. 20 need not be performed in numericalsequence, unless described otherwise. Further, the use of the term“Step” is a convenient nomenclature defining the process herein, and,unless otherwise stated herein, is not meant to invoke the provisions of35 U.S.C. § 112, paragraph 6.

In a process block 292, the articulator is moved according to Step 1data to position the first support member at the first support location.In a process block 294, the articulator is moved according to Step 2data to position the second support member at the second supportlocation. In a process block 296, the articulator is moved according toStep 3 data to position the third support member at the third supportlocation.

In a process block 298, the process 290 can pause to allow positioningof the actual example object on the three support members. In oneembodiment, the object can be placed on the support member manually.Other methods of object placement (such as automated ormachine-assisted) are possible.

In a process block 300, the articulator is moved according to Step 5data to measure the first section of the object placed on the supportmembers. For the example object, the first section is one of the two endsections of the object. In a process block 302, the articulator is movedaccording to Step 6 data to measure the first outer end of the object.In a process block 304, the articulator is moved according to Step 7data to measure the second section of the object. In a process block306, the articulator is moved according to Step 8 data to measure thethird section of the object. In a process block 308, the articulator ismoved according to Step 9 data to measure the fourth section of theobject. In a process block 310, the articulator is moved according toStep 10 data to measure the fifth section of the object. In a processblock 312, the articulator is moved according to Step 11 data to measurethe sixth section of the object. For the example object the sixthsection is the other of the two end sections of the object. In a processblock 314, the articulator is moved according to Step 12 data to measurethe second outer end of the object. In one embodiment, such sectionmeasurements can be used to project the sections so as to determine theintersection points.

FIG. 21 shows one embodiment of a process 320 that can be performed bythe controller to compare the object measurements with the definitiondata. In a process block 322, measurements for the object are obtained.In one embodiment, such measurements can be obtained via the exampleprocess 290 of FIG. 20. In a process block 324, the measurements arecompared with the object definition data. In a process block 326, apost-comparison operation can be performed if needed or desired. Forexample, if the comparison shows that the measured object deviates insome manner from the definition data beyond some amount, such deviationcan be identified so as to allow correction(s) to the fabricationprocess.

FIG. 22 shows another example of the post-comparison operation that canbe performed by the controller. In a process block 332, one or morecutoff locations on the actual object are determined based on thecomparison of the measurement and the definition data. For the exampleobject, two cutoff locations are determined to allow cutting of two tabsat the ends of the object. Such cutoff locations on the actual objectcan be the locations corresponding to the outer end definition points inthe definition data. In a process block 334, the articulator is moved toacquire a marker from a known location and mark the cutoff locations onthe object. In one embodiment, the marker can be stored in the markerholder 190 whose location is known.

FIGS. 23-26 show some embodiments of the support members. FIG. 23A showsone embodiment of the support member 184 in its storage configuration340, positioned at its nesting location 282, and with itsheight-adjustment member retracted. FIG. 23B shows the support member184 in its deployed configuration 350, at its designated location, withits height-adjustment member raised so as to provide its supportlocation 186.

FIG. 24 shows a cutaway view of one embodiment of a support member 360that is similar to the example support member 184 of FIGS. 23A and 23B.The support member 360 is shown as having retractable member 370 thatcan be raised up or down. In one embodiment, a cross bar 364 can bemounted to the end of the retractable member 370. The cross bar 364 canbe dimensioned to be engaged by the articulator (not shown) so as toallow up and/or down movement of the cross bar 364. In one embodiment, aV-nest member 366 can be mounted to the cross bar 364, and the V-nestmember 366 can be dimensioned to provide a support location for theobject being supported. Thus, the up and/or down movement of the crossbar 364 (via the articulator or otherwise) results in similar movementof the V-nest member 366. The V-nest member 366 can be suited forreceiving objects such as rod-like or tubular objects (such as theexample object shown in FIG. 9). It will be understood, however, thatthe object engaging member 366 can be dimensioned in any manner toengage different shaped objects.

In one embodiment, the retractable member 370 can be similar to a metaltape (used for tape measures), and can be wound into a tape spool 372within a housing 358. The spool 372 can be provided with a rewindtorsion spring so as to facilitate rewinding of the tape (and thuslowering of a V-nest 366) when the support member 360 is not in use. Inother embodiments, the retractable member 370 can comprise a differentstructure, such as a spar or tubular metal member that can be retractedor advanced. In some embodiments, the retractable member is not woundonto a spool.

In one embodiment, the support member 360 can include a retractionblocking member 374 (for example a rubber ball). In one configuration,the blocking member 374 is shown to be wedged against the tape 370 and ablock 376, thereby inhibiting the tape 370 from being retracted. Such afeature can be used after the articulator moves the cross bar 364upwards to position the V-nest member 366 at a selected height. In oneconfiguration, the blocking member 374 can be moved (indicated by anarrow 378) away from the wedged configuration, thereby allowingretraction of the tape 370. In one embodiment, the disengagement of theblocking member 374 can be achieved manually (for example, by turningthe support member upside-down).

In one embodiment, as shown in FIG. 24, the housing 358 can be mountedon a base 368. The base 368 can be configured to provide stability forthe support member 360. In one embodiment, a cross bar 362 can also bemounted on the housing 358 so t as to allow the articulator to move thesupport member 360 as a whole.

FIGS. 25A and 25B show one embodiment of a support member 380 where theretraction inhibiting/allowing functionality can be facilitated by thearticulator. The articulator can be provided with signals from thecontroller so as to achieve such functionality.

In one embodiment, the support member 380 includes a movable blockingmember 400 that can be pivotably mounted to a housing 384 or some otherstructure that is substantially stationary with respect to the housing384. The example blocking member 400 is shown to have an engaging end402 and a control end 404, so that movement of the control end 404results in corresponding movement of the engaging end 402 about a pivot406.

In FIG. 25A, the engaging end 402 of the blocking member 400 is shown toengage the tape 390 and push the tape against a block 410, therebyinhibiting downward movement of the tape through a tape pathway 392. Inone embodiment, the blocking member 400 can be spring biased in aselected manner. For example, a spring 408 is shown to be oriented so asto provide spring coupling between the engaging end portion of theblocking member 400 with the housing 384. Thus, when the spring 408 isin its relaxed configuration, the engaging end 402 of the blockingmember 400 engages the tape 390 to inhibit the F downward movement ofthe tape 390. In such a configuration, the tape 390 can be moved upward(via the articulator, for example), since the upward movement of thetape 390 can result in the engaging end 402 giving due to slightcompression of the spring 408. However, once the upward movement stops,the downward movement of the tape 390 is inhibited.

In FIG. 25B, the engaging end 402 of the blocking member 400 is shown tobe disengaged from the tape 390, thereby allowing the downward (as wellas upward) movement (indicated as an arrow 382) of the tape 390. Suchdisengagement of the blocking member 400 can be achieved by moving thecontrol end 404. The movement of the control end 404 can be effectuatedmanually, via the articulator, or any combination thereof.

As shown in FIG. 25B, the spring 408 becomes compressed when theblocking member 400 is in the disengagement configuration. Once the tape390 becomes retracted in such a mode, the control end 404 can bereleased, and the blocking member 400 will return to the engagementconfiguration of FIG. 25A due to the action of the spring 408.

FIGS. 26A and 26B show by examples that in some embodiments, supportmembers can be configured in other ways to provide differentfunctionalities that can be desirable. For example, a support member canbe configured to provide additional stability when at its supportlocation. In another example, a support member can be configured tofacilitate its easy return to its nesting position from the supportlocation.

FIG. 26A shows a top view of one embodiment of a support member 420having a housing with a retractable member (tape, for example) therein.The support member 420 is further shown to have first and second crossbars 422 and 424. The first cross bar 422 engages with the articulatorto facilitate movement of the support member 420 as a whole. The secondcross bar 424 is coupled to the retractable member and engages with thearticulator to facilitate up and/or down movement of the object engagingmember (V-nest, for example). The support member 420 is further shown toinclude a base 430 that provides stability of the support member 420.

In one embodiment, the support member can include a stability enhancingmember 440, and a return facilitating member 432. In one embodiment, thestability enhancing member 440 includes an electromagnet 440 that ispowered via a power cord 442. The power cord 442 can be secured via abulkhead 444 so as to relieve stress on the cord coupling at theelectromagnet 440.

As shown in FIG. 26A, the electromagnet 440 is shown to be turned “ON,”when the support member 420 is in its support location, therebyproviding additional downward force against a metallic table top. Thus,when the electromagnet 440 is energized, the stability of the supportmember can be enhanced. In one embodiment, the electromagnet can bepowered at or about the support member 420 (via the articulator, forexample), or from the power source (not shown) either manually or underthe control of the controller.

For the purpose of description of FIGS. 26A and 26B, it will be assumedthat the metallic table top has at least some magnetic material. Ofcourse, not all table tops or other support surfaces are magnetic. Otherstability-enhancing techniques—such as bases having suctioncapability—are contemplated.

When the supporting function of the support member 420 is completed, theelectromagnet can be turned off, thereby allowing the support member 420to be moved back to its nesting location easier. In one embodiment, thesupport member 420 can be pulled back into the nesting location byretraction of the power cord (or some other cord) 422.

FIG. 26B shows that in one embodiment, a nesting assembly 450 can beconfigured to provide such retraction of the cord 442. For example pinchrollers 454 a and 454 b can engage the cord 442 and rotate (clockwisefor the roller 454 a, and counterclockwise for the roller 454 b),thereby pulling the support member 420 into the nesting assembly 450.When the support member 420 is to be deployed from the nesting assembly450, the pinch rollers 454 a and 454 b can disengage from the cord 442,thereby allowing the cord 442 to move with the support member 420.

In one embodiment, as shown in FIGS. 26A and 26B, the support member 420and the nesting assembly 450 can be configured to facilitate repeatableand accurate positioning of the support member 420 at the nestingassembly 450. In one embodiment, the base 430 can be dimensioned todefine the return facilitating member 432. In one embodiment, the returnfacilitating member 432 can define tapers 434 a and 434 b. The nestingassembly 450 can also be dimensioned to define taper receiving surfaces452 a and 452 b. Thus, when the taper 434 of the base 430 is pulled intothe space defined by the taper receiving surfaces 452 a and 452 b,mating of the tapers to their respective receiving surfaces (taper 434 ato surface 452 a, and taper 434 b to surface 452 b) facilitates accuratepositioning of the support member 420 at the nesting assembly 450. Itwill be understood that other configurations are possible.

FIGS. 27-31 show how some features of the present disclosure can beconfigured to accommodate situations where the actual object deviatessignificantly from the definition data. FIG. 27A shows an examplesituation 470 where an actual object 472 can deviate significantly fromthe definition data (depicted as 210). The articulator is shown to beperforming measurements at example locations 476 a, 476 b, and 476 c.For the purpose of description, the articulator is depicted as havingexample prongs 478 a and 478 b that move about the object 470 accordingto the definition data 210.

The example situation 470 shows that in one embodiment, the examplesupport locations 186 a, 186 b, and 186 c (based on the definition data210) can be adjusted to new support locations (depicted as 474 a, 474 b,and 474 c) to accommodate the deviation of the object 472 from thedefinition data 210. In some situations, the articulator may be able tohandle deviations to some degree without having to adjust the supportlocations. FIG. 27A shows a concept where one or more of the supportlocations can be adjusted from those defined by the definition data toaccount for some deviation of the object so as to facilitate measurementof the object.

FIG. 27B shows an example situation 480 where the deviation of an object482 can be substantial such that support location adjustments alone maynot be enough to allow proper measurements. Even if support locationscan be adjusted, it may be desirable to make other adjustments toaccommodate the substantial deviation of the object 480.

FIG. 27B further shows examples of how the deviation of the object 482(from the definition data 210) can lead to problems in measurementmovements based on the definition data 210. An example measurement 484a, where the articulator prongs 478 a and 478 b are able to accommodatethe first section of the object 482, is not problematic, since the firstsection of the object 482 is depicted as being generally aligned withthe corresponding section of the definition data 210.

However, in another example measurement 484 b where the prongs 478 aredepicted as being centered with respect to the second section of thedefinition data 210, the second section of the object 482 is depicted asbeing deviated sufficiently so that one of the prongs 478 b can touchthe object 482. If the prongs 478 attempt to move based on thedefinition data 210 (for example, from left to right in FIG. 27B), thenthe second section of the object 482 will inhibit further movement. Sucha situation can result in damages to the articulator, the object 482, orboth.

In another example measurement 484 c where the prongs 478 are depictedas being centered with respect to the last section of the definitiondata 210, the last section of the object 482 is depicted as beingdeviated even further (than the example second section) so that theprongs 478 miss that section altogether.

Based on the description of FIGS. 27A and 27B, one can see that acapability to handle deviations of objects from their definition datacan be useful and desirable. While the example objects 470 and 480 inFIGS. 27A and 27B were rod-like objects, it will be understood that theconcept of adjusting to accommodate for deviation can be applied to anyother shaped objects that can be measured by the articulator.

FIG. 28 shows one embodiment of a process 490 that can provide theforegoing functionality of adjusting to accommodate deviations inobjects. In a process block 492, deviation of an object from thedefinition data is detected. Such detection can be achieved in a numberof ways. For example, the deviation may be sufficiently apparent to anoperator. In another example, the articulator can be configured to sensecontact with some object. If such contact is unexpected, the nature ofthe contact can be verified, for example, by the operator. In a processblock 494, corrective action is performed to account for the deviation.

FIG. 29 shows one embodiment of a process 500 that can perform thecorrective action of the process 490 of FIG. 28. In a process block 502,deviation is detected. In a process block 504, adjustments to supportlocations can be determined to accommodate the deviation. In a processblock 506, adjustments of the support locations can be facilitated. Inone embodiment, the support members can be adjusted to provide suchadjustments of the support locations. In one embodiment, adjustment(s)of the support location(s) can be performed by the operator,automatically by the articulator under the control of the controller, orany combination thereof.

FIG. 30 shows one embodiment of a process 510 that can perform thecorrective action of the process 490 of FIG. 28. In a process block 512,deviation is detected. In a process block 514, adjustments tomeasurement movements of the articulator are determined to accommodatethe deviation. In a process block 516, measurement movements areeffectuated based on the adjusted measurement movement data orinstruction.

FIG. 31 shows one embodiment of a process 520 that can be an example ofthe process 510 of FIG. 30. In this example, one of the sections ispositioned so as to be measurable according to movement data that isbased on the definition data. Thus, the example situation shown in FIG.27B can apply to the example process 520. Measurement movements for thesecond section are adjusted based on the measurement of the firstsection, and so on. For the purpose of description of FIG. 31, “nominaldata” refers to the measurement movement data or instruction that can beadjusted.

In a process block 522, measurement movement data based on thedefinition data is set as the nominal data. In a process block 524, thefirst section is measured to obtain first centerline information. In aprocess block 526, the nominal data is adjusted so as to conform to thefirst centerline. In a process block 528, the first end (intersectionpoint between the first and second sections) is determined based on theadjusted nominal data. In a process block 530, the nominal data isadjusted based on the first end determination. In on embodiment, thenominal data is adjusted so that the unadjusted first end information(along with the remaining data for subsequent sections and ends) undergoa 3D transformation so as to yield adjusted first end information thatcoincides with the first end determined in the process block 528. In aprocess block 532, the second section is measured based on the first endof the adjusted nominal data to obtain second centerline information. Ina process block 534, the nominal data is adjusted so as to conform tothe second centerline. In a process block 536, the second end(intersection point between the second and third sections) is determinedbased on the adjusted nominal data. In a process block 538, the nominaldata is adjusted based on the second end determination. As shown in aprocess block 540, measurements of subsequent sections and adjustmentscan be performed in a similar manner.

Listing of Example Data

Sample data for an example process 290 illustrated in FIG. 20 anddescribed above are displayed below. In the example data listed, eachmovement instruction for articulator movement has 19 entries as follows:

1-3: X, Y, Z

4-6: cosines projections on X-axis

7-9: cosines of projections on Y-axis

10-12: cosines of projections on Z-axis

13: elbow offset

14-16: uvw offset

17: speed (mm/s)

18: pre-process dwell time (ms)

19: control code STEP: 1 ROBO REFERENCE: ˜1977 +877.094 +186.137+272.799 +0.707104 +0.000076 +0.707109 −0.028273 +0.999203 +0.028165−0.706544 −0.039908 +0.706543 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0+938.612 +187.491 +93.426 +0.258782 +0.016631 +0.965792 −0.004305+0.999862 −0.016065 −0.965926 −0.000001 +0.258818 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 +962.585 +187.498 +117.352 +0.069752 +0.011107+0.997503 −0.000775 +0.999938 −0.011080 −0.997564 −0.000000 +0.069756+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +994.992 +187.560 +114.978+0.034900 +0.000230 +0.999391 −0.000008 +1.000000 −0.000230 −0.999391+0.000000 +0.034900 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +1024.995+187.535 +114.969 −0.000001 −0.009372 +0.999956 +0.000000 +0.999956+0.009372 −1.000000 +0.000000 −0.000001 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +1031.836 +187.506 +172.328 −0.000001 −0.017445 +0.999848+0.000000 +0.999848 +0.017445 −1.000000 +0.000000 −0.000001 +0.000+0.000 +0.000 +0.000 75.00 1.00 0 +1024.922 +187.493 +160.191 +0.069749−0.015740 +0.997440 +0.001097 +0.999876 +0.015702 −0.997564 −0.000001+0.069757 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +1024.927 +187.502+155.284 +0.069748 −0.015169 +0.997449 +0.001058 +0.999885 +0.015132−0.997564 +0.000000 +0.069756 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+995.017 +187.447 +157.516 +0.069757 −0.005408 +0.997549 +0.000376+0.999985 +0.005395 −0.997564 −0.000001 +0.069758 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +962.586 +187.478 +159.704 +0.069755 +0.005975+0.997546 −0.000417 +0.999982 −0.005960 −0.997564 −0.000000 +0.069756+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +874.837 +185.706 +167.450+1.000000 −0.000003 −0.000001 +0.000003 +0.998489 +0.054951 +0.000001−0.054951 +0.998489 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +887.679+186.028 +106.887 +0.998630 +0.000001 +0.052336 −0.002388 +0.998959+0.045546 −0.052282 −0.045608 +0.997590 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +898.355 +185.923 +102.429 +0.999391 −0.000002 +0.034899−0.001684 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+0.00075.00 0.00 64 +725.344 +214.482 +67.396 −0.778366 +0.627811 +0.000000−0.627552 −0.778046 −0.028685 −0.018008 −0.022327 +0.999589 +0.000+0.000 +0.000 +0.000 75.00 1.00 64 +725.202 +214.261 +75.511 −0.778366+0.627810 +0.000000 −0.627461 −0.777933 −0.033341 −0.020932 −0.025951+0.999444 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +724.967 +213.967+83.627 −0.778366 +0.627810 +0.000000 −0.627357 −0.777805 −0.037982−0.023845 −0.029564 +0.999278 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64+724.686 +213.614 +91.740 −0.778366 +0.627810 +0.000000 −0.627239−0.777658 −0.042664 −0.026785 −0.033208 +0.999089 +0.000 +0.000 +0.000+0.000 75.00 0.00 64 +724.468 +213.335 +106.729 −0.778366 +0.627811+0.000000 −0.626958 −0.777310 −0.052086 −0.032700 −0.040542 +0.998643+0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +722.175 +215.236 +117.151−0.777323 +0.626969 −0.051751 −0.624956 −0.779012 −0.050702 −0.072103−0.007070 +0.997372 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +715.917+216.812 +229.744 −0.777324 +0.626969 −0.051750 −0.616826 −0.775744−0.133216 −0.123667 −0.071631 +0.989735 +0.000 +0.000 +0.000 +0.000150.00 0.00 64 +899.859 +184.880 +282.187 +1.000000 −0.000004 −0.000002+0.000004 +0.996764 +0.080387 +0.000002 −0.080387 +0.996764 +0.000+0.000 +0.000 +0.000 150.00 0.00 64 STEP: 2 ROBO REFERENCE: ˜1977+877.090 −185.632 +272.783 +0.707102 −0.000103 +0.707111 +0.038913+0.998490 −0.038767 −0.706040 +0.054929 +0.706039 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 +938.658 −187.454 +93.622 +0.258785 −0.015347+0.965813 +0.003977 +0.999882 +0.014823 −0.965927 +0.000005 +0.258816+0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +962.584 −187.495 +117.339+0.069754 −0.008421 +0.997529 +0.000587 +0.999965 +0.008401 −0.997564+0.000000 +0.069756 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +995.010−187.568 +115.039 +0.034898 +0.005369 +0.999376 −0.000188 +0.999986−0.005366 −0.999391 −0.000000 +0.034898 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +1025.006 −187.538 +115.050 −0.000003 +0.017548 +0.999846−0.000000 +0.999846 −0.017548 −1.000000 −0.000000 −0.000003 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +1033.021 −187.510 +184.134 −0.000002+0.030279 +0.999541 −0.000000 +0.999541 −0.030279 −1.000000 −0.000000−0.000002 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +1024.916 +187.490+171.982 +0.069732 +0.027806 +0.997178 −0.001938 +0.999613 −0.027739−0.997564 +0.000001 +0.069759 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0+1024.930 −187.501 +167.141 +0.069731 +0.027036 +0.997199 −0.001886+0.999634 −0.026970 −0.997564 −0.000000 +0.069756 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +995.002 −187.453 +169.306 +0.069753 +0.014648+0.997457 −0.001020 +0.999893 −0.014612 −0.997564 +0.000002 +0.069760+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +962.583 −187.394 +171.680+0.069757 +0.000340 +0.997564 −0.000023 +1.000000 −0.000339 −0.997564+0.000001 +0.069757 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +874.853−185.028 +167.407 +1.000000 +0.000003 −0.000002 −0.000003 +0.997134−0.075651 +0.000001 +0.075651 +0.997134 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +887.581 −185.435 +106.849 +0.998629 −0.000001 +0.052337+0.003315 +0.997994 −0.063228 −0.052232 +0.063315 +0.996626 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +898.414 −185.327 +102.398 +0.999391+0.000002 +0.034898 +0.002331 +0.997762 −0.066820 −0.034820 +0.066860+0.997155 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +903.482 −185.863+84.386 +0.999848 +0.000001 +0.017452 +0.001164 +0.997771 −0.066719−0.017413 +0.066729 +0.997619 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+907.645 −186.407 +76.350 +0.999848 +0.000000 +0.017452 +0.001165+0.997766 −0.066797 −0.017413 +0.066807 +0.997614 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +911.913 −186.937 +68.106 +1.000000 +0.000001−0.000001 −0.000001 +0.997665 −0.068299 +0.000001 +0.068299 +0.997665+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +800.117 −187.510 +59.999+1.000000 −0.000001 +0.000000 +0.000001 +0.999535 −0.030503 −0.000000+0.030503 +0.999535 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +678.580−342.769 +51.499 +0.186658 +0.982425 +0.000000 −0.981966 +0.186571−0.030548 −0.030011 +0.005702 +0.999533 +0.000 +0.000 +0.000 +0.00075.00 0.00 64 +683.090 −319.050 +57.938 +0.186658 +0.982425 +0.000000−0.982072 +0.186591 −0.026787 −0.026316 +0.005000 +0.999641 +0.000+0.000 +0.000 +0.000 75.00 0.00 64 +682.824 −318.990 +66.060 +0.186658+0.982425 +0.000000 −0.981933 +0.186564 −0.031649 −0.031092 +0.005907+0.999499 +0.000 +0.000 +0.000 +0.000 75.00 1.00 64 +682.558 −318.957+74.172 +0.186658 +0.982425 +0.000000 −0.981765 +0.186532 −0.036649−0.036005 +0.006841 +0.999328 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64+682.158 −318.883 +82.286 +0.186658 +0.982425 +0.000000 −0.981574+0.186496 −0.041605 −0.040874 +0.007766 +0.999134 +0.000 +0.000 +0.000+0.000 75.00 0.00 64 +681.615 −318.765 +90.401 +0.186658 +0.982425+0.000000 −0.981362 +0.186456 −0.046504 −0.045687 +0.008680 +0.998918+0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +681.283 −318.700 +105.384+0.186657 +0.982425 +0.000000 −0.980842 +0.186356 −0.056755 −0.055757+0.010594 +0.998388 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +681.697−315.823 +116.060 +0.186426 +0.981201 −0.049903 −0.981182 +0.183342−0.060554 −0.050267 +0.060253 +0.996917 +0.000 +0.000 +0.000 +0.00075.00 0.00 64 +679.607 −309.073 +241.379 +0.186425 +0.981201 −0.049903−0.970604 +0.176065 −0.164100 −0.152228 +0.079029 +0.985181 +0.000+0.000 +0.000 +0.000 150.00 0.00 64 +899.909 −183.955 +282.101 +1.000000+0.000002 −0.000002 −0.000003 +0.994064 −0.108800 +0.000002 +0.108800+0.994064 +0.000 +0.000 +0.000 +0.000 150.00 0.00 64 STEP: 3 ROBOREFERENCE: ˜1977 +877.079 +62.219 +272.829 +0.707107 +0.000009 +0.707107−0.005450 +0.999970 +0.005438 −0.707086 −0.007699 +0.707086 +0.000+0.000 +0.000 +0.000 150.00 0.00 0 +938.620 +62.498 +93.457 +0.258815+0.005354 +0.965912 −0.001386 +0.999986 −0.005171 −0.965926 −0.000000+0.258819 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +962.589 +62.499+117.101 +0.069756 +0.003994 +0.997556 −0.000279 +0.999992 −0.003984−0.997564 −0.000000 +0.069756 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+994.999 +62.500 +114.965 +0.034900 +0.001353 +0.999390 −0.000047+0.999999 −0.001353 −0.999391 +0.000000 +0.034900 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +1025.000 +62.500 +115.025 −0.000000 −0.000962+1.000000 +0.000000 +1.000000 +0.000962 −1.000000 +0.000000 −0.000000+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +1035.244 +62.503 +206.307−0.000000 −0.004086 +0.999992 +0.000000 +0.999992 +0.004086 −1.000000+0.000000 −0.000000 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +1024.918+62.497 +194.206 +0.069756 −0.003445 +0.997558 +0.000240 +0.999994+0.003437 −0.997564 −0.000000 +0.069757 +0.000 +0.000 +0.000 +0.00075.00 1.00 0 +1024.933 +62.500 +189.431 +0.069756 −0.003298 +0.997559+0.000230 +0.999995 +0.003290 −0.997564 +0.000000 +0.069756 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +995.002 +62.500 +191.465 +0.069756−0.001013 +0.997564 +0.000071 +0.999999 +0.001011 −0.997564 −0.000000+0.069756 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +962.585 +62.495+193.779 +0.069756 +0.001662 +0.997563 −0.000116 +0.999999 −0.001658−0.997564 −0.000000 +0.069756 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+874.866 +62.113 +167.498 +1.000000 −0.000001 −0.000000 +0.000001+0.999929 +0.011932 +0.000000 −0.011932 +0.999929 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +887.633 +62.184 +106.916 +0.998630 +0.000000+0.052336 −0.000510 +0.999953 +0.009718 −0.052334 −0.009731 +0.998582+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +898.389 +62.164 +102.468+0.999391 −0.000000 +0.034899 −0.000362 +0.999946 +0.010371 −0.034898−0.010377 +0.999337 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +903.524+62.248 +84.439 +0.999848 −0.000000 +0.017452 −0.000180 +0.999947+0.010338 −0.017451 −0.010340 +0.999794 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +907.670 +62.318 +76.384 +0.999848 −0.000000 +0.017452−0.000180 +0.999947 +0.010338 −0.017451 −0.010339 +0.999794 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +911.912 +62.409 +68.124 +1.000000−0.000000 −0.000000 +0.000000 +0.999944 +0.010590 +0.000000 −0.010590+0.999944 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +800.118 +62.499+60.000 +1.000000 +0.000000 +0.000000 −0.000000 +0.999994 +0.003425−0.000000 −0.003425 +0.999994 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64+615.637 −107.686 +63.109 +0.269462 +0.963011 +0.000000 −0.952962+0.266650 +0.144084 +0.138754 −0.038825 +0.989566 +0.000 +0.000 +0.000+0.000 75.00 0.00 64 +622.358 −83.675 +60.911 +0.269468 +0.963009−0.000000 −0.953344 +0.266764 +0.141322 +0.136095 −0.038082 +0.989964+0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +623.465 −83.975 +68.947+0.269468 +0.963009 +0.000000 −0.954319 +0.267036 +0.134038 +0.129079−0.036119 +0.990976 +0.000 +0.000 +0.000 +0.000 75.00 1.00 64 +624.406−84.238 +77.013 +0.269468 +0.963009 +0.000000 −0.955235 +0.267292+0.126811 +0.122120 −0.034171 +0.991927 +0.000 +0.000 +0.000 +0.00075.00 0.00 64 +625.235 −84.469 +85.093 +0.269467 +0.963010 +0.000000−0.956100 +0.267534 +0.119575 +0.115152 −0.032221 +0.992825 +0.000+0.000 +0.000 +0.000 75.00 0.00 64 +625.952 −84.668 +93.186 +0.269467+0.963010 +0.000000 −0.956915 +0.267762 +0.112328 +0.108173 −0.030269+0.993671 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64 +625.591 −84.559+108.227 +0.269468 +0.963009 +0.000000 0.958100 +0.268094 +0.100850+0.097119 −0.027176 +0.994902 +0.000 +0.000 +0.000 +0.000 75.00 0.00 64+626.057 −81.584 +118.603 +0.269095 +0.961689 −0.052375 −0.957809+0.272916 +0.090099 +0.100942 +0.025919 +0.994555 +0.000 +0.000 +0.000+0.000 75.00 0.00 64 +623.560 −72.963 +264.254 +0.269096 +0.961688−0.052375 −0.962312 +0.266257 −0.055338 −0.039273 +0.065292 +0.997093+0.000 +0.000 +0.000 +0.000 150.00 0.00 64 +699.911 +61.918 +282.289+1.000000 −0.000001 −0.000000 +0.000001 +0.999839 +0.017930 +0.000000−0.017930 +0.999839 +0.000 +0.000 +0.000 +0.000 150.00 0.00 64 STEP: 5ROBO REFERENCE: ˜1977 +611.659 −315.901 +271.860 +0.703125 +0.711066+0.000000 −0.704924 +0.697052 −0.131152 −0.093258 +0.092216 +0.991362+0.000 +0.000 +0.000 +0.000 300.00 0.00 0 +612.763 −316.994 +225.678+0.703125 +0.711066 +0.000000 −0.708574 +0.700661 −0.083642 −0.059475+0.058811 +0.996496 +0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +614.676−318.897 +193.295 +0.703125 +0.711066 +0.000000 −0.709996 +0.702067−0.054831 −0.038989 +0.038553 +0.998496 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +615.480 −319.658 +169.655 +0.703125 +0.711066 −0.000000−0.710649 +0.702713 −0.034248 −0.024353 +0.024081 +0.999413 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +614.675 −318.897 +193.295 +0.703125+0.711066 −0.000000 −0.709996 +0.702067 −0.054831 −0.038988 +0.038553+0.998496 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +612.760 −316.997+225.678 +0.703125 +0.711066 −0.000000 −0.708574 +0.700661 −0.083641−0.059474 +0.058810 +0.996496 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+611.650 −315.909 +271.860 +0.703125 +0.711066 −0.000000 −0.704924+0.697052 −0.131148 −0.093255 +0.092213 +0.991363 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 +677.807 −247.562 +271.710 +0.703127 +0.711064−0.000001 −0.701665 +0.693833 −0.162055 −0.115231 +0.113946 +0.986782+0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +678.863 −248.554 +225.565+0.703125 +0.711067 +0.000000 −0.706107 +0.698220 −0.117902 −0.083837+0.082900 +0.993025 +0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +681.635−251.277 +193.291 +0.703125 +0.711066 +0.000000 −0.708027 +0.700119−0.092364 −0.065677 +0.064944 +0.995725 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +683.173 −252.829 +169.726 +0.703125 +0.711066 +0.000000−0.709100 +0.701181 −0.074311 −0.052840 +0.052250 +0.997235 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +681.630 −251.281 +193.291 +0.703125+0.711066 −0.000000 −0.708027 +0.700120 −0.092360 −0.065674 +0.064941+0.995726 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +678.844 −248.570+225.565 +0.703126 +0.711066 −0.000000 −0.706107 +0.698223 −0.117889−0.083827 +0.082891 +0.993027 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+677.807 −247.565 +271.710 +0.703126 +0.711065 −0.000001 −0.701666+0.693832 −0.162056 −0.115232 +0.113947 +0.986782 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 STEP: 6 ROBO REFERENCE: ˜1977 +576.804 −351.746+271.913 +0.703122 +0.711070 +0.000000 −0.706063 +0.698171 −0.118457−0.084231 +0.083290 +0.992959 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0+579.533 −354.454 +193.294 +0.703125 +0.711066 −0.000000 −0.710511+0.702576 −0.039507 −0.028092 +0.027778 +0.999219 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +614.670 −318.905 +193.295 +0.703125 +0.711067−0.000000 −0.709997 +0.702067 −0.054830 −0.038988 +0.038552 +0.998496+0.000 +0.000 +0.000 +0.000 75.00 0.50 1 +623.602 −309.865 +193.295+0.703125 +0.711066 +0.000000 −0.709817 +0.701890 −0.059255 −0.042135+0.041664 +0.998243 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +614.679−318.893 +193.295 +0.703125 +0.711066 +0.000000 −0.709996 +0.702067−0.054833 −0.038990 +0.038554 +0.998496 +0.000 +0.000 +0.000 +0.00075.00 1.00 0 +579.547 −354.438 +193.294 +0.703126 +0.711066 +0.000000−0.710511 +0.702576 −0.039511 −0.028095 +0.027781 +0.999219 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +576.794 −351.750 +271.913 +0.703125+0.711066 −0.000000 −0.706060 +0.698175 −0.118449 −0.084225 +0.083285+0.992960 +0.000 +0.000 +0.000 +0.000 150.00 0.50 0 STEP: 7 ROBOREFERENCE: ˜1977 +701.934 −220.570 +281.411 −0.413873 +0.811253+0.413010 −0.910312 −0.365599 −0.194088 −0.006458 −0.456295 +0.889805+0.000 +0.000 +0.000 +0.000 300.00 0.00 0 +694.792 −203.033 +239.410−0.413910 +0.811243 +0.412993 −0.909504 −0.387708 −0.149948 +0.038476−0.437684 +0.898305 +0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +693.527−188.745 +210.244 −0.413916 +0.811237 +0.412998 −0.907974 −0.400433−0.123435 +0.065243 −0.426083 +0.902328 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +692.191 −178.544 +188.887 −0.413907 +0.811240 +0.413001−0.906387 −0.409387 −0.104234 +0.084519 −0.417482 +0.904746 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +693.452 −188.683 +210.284 −0.413871+0.811255 +0.413009 −0.907992 −0.400410 −0.123380 +0.065281 −0.426072+0.902331 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +694.660 −202.864+239.503 −0.413864 +0.811256 +0.413013 −0.909522 −0.387700 −0.149862+0.038549 −0.437667 +0.898310 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+701.882 −220.489 +281.453 −0.413862 +0.811253 +0.413022 −0.910317−0.365600 −0.194060 −0.006431 −0.456295 +0.889805 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 +672.156 −161.069 +311.687 −0.414001 +0.811206+0.412975 −0.910264 −0.371303 −0.183174 +0.004747 −0.451751 +0.892132+0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +664.981 −143.455 +269.714−0.413883 +0.811254 +0.412999 −0.908736 −0.395027 −0.134730 +0.053846−0.431070 +0.900711 +0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +663.271−129.378 +240.460 −0.413905 +0.811242 +0.413001 −0.906448 −0.409086−0.104881 +0.083869 −0.417775 +0.904671 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +661.247 −119.451 +219.055 −0.413902 +0.811242 +0.413003−0.904151 −0.419087 −0.082925 +0.105812 −0.407739 +0.906947 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +663.211 −129.314 +240.499 −0.413878+0.811252 +0.413007 −0.906458 −0.409074 −0.104842 +0.083897 −0.417765+0.904673 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +664.881 −143.265+269.811 −0.413879 +0.811250 +0.413010 −0.908735 −0.395044 −0.134687+0.053893 −0.431060 +0.900712 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+671.977 −160.946 +311.763 −0.413890 +0.811242 +0.413015 −0.910314−0.371234 −0.183067 +0.004813 −0.451743 +0.892135 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 STEP: 8 ROBO REFERENCE: ˜1977 +645.545 −55.427+320.056 −0.017379 +0.961159 −0.275447 −0.989486 −0.056094 −0.133306−0.143579 +0.270235 +0.952028 +0.000 +0.000 +0.000 +0.000 300.00 0.00 0+647.584 −68.110 +275.692 −0.017398 +0.961158 −0.275450 −0.995868−0.041216 −0.080919 −0.089129 +0.272904 +0.957904 +0.000 +0.000 +0.000+0.000 75.00 0.00 1 +650.403 −76.972 +244.562 −0.017399 +0.961158−0.275449 −0.998295 −0.032051 −0.048781 −0.055715 +0.274131 +0.960077+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +651.382 −83.467 +221.832−0.017397 +0.961158 −0.275449 −0.999348 −0.025428 −0.025613 −0.031622+0.274823 +0.960975 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +650.448−76.974 +244.560 −0.017369 +0.961159 −0.275447 −0.998293 −0.032035−0.048836 −0.055763 +0.274129 +0.960075 +0.000 +0.000 +0.000 +0.00075.00 1.00 0 +647.641 −68.101 +275.688 −0.017367 +0.961160 −0.275447−0.995863 −0.041202 −0.080984 −0.089188 +0.272901 +0.957899 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +645.563 −55.418 +320.054 −0.017371+0.961160 −0.275446 −0.989484 −0.056091 −0.133324 −0.143596 +0.270233+0.952026 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +645.042 +13.942+300.277 −0.017366 +0.961160 −0.275446 −0.992439 −0.050048 −0.112073−0.121505 +0.271417 +0.954761 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0+647.042 +1.262 +255.868 −0.017384 +0.961159 −0.275448 −0.997571−0.035260 −0.060079 −0.067458 +0.273735 +0.959437 +0.000 +0.000 +0.000+0.000 75.00 0.00 1 +649.220 −7.649 +224.690 −0.017362 +0.961159−0.275448 −0.999287 −0.025916 −0.027448 −0.033520 +0.274775 +0.960924+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +649.491 −14.152 +201.946−0.017374 +0.961159 −0.275448 −0.999811 −0.019093 −0.003560 −0.008680+0.275334 +0.961309 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +649.172−7.635 +224.691 −0.017395 +0.961158 −0.275448 −0.999288 −0.025933−0.027386 −0.033465 +0.274776 +0.960926 +0.000 +0.000 +0.000 +0.00075.00 1.00 0 +647.001 +1.268 +255.868 −0.017408 +0.961158 −0.275450−0.997573 −0.035271 −0.060029 −0.067412 +0.273736 +0.959439 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +645.009 +13.945 +300.276 −0.017383+0.961159 −0.275448 −0.992443 −0.050055 −0.112032 −0.121468 +0.271419+0.954766 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0 STEP: 9 ROBOREFERENCE: ˜1977 +655.196 +34.266 +298.543 +0.522857 +0.845297 +0.109967−0.840531 +0.532728 −0.098537 −0.141875 −0.040910 +0.989039 +0.000+0.000 +0.000 +0.000 300.00 0.00 0 +659.212 +37.827 +252.593 +0.522859+0.845296 +0.109967 −0.846182 +0.530274 −0.052789 −0.102935 −0.065451+0.992532 +0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +662.488 +39.932+220.333 +0.522859 +0.845296 +0.109967 −0.848823 +0.528140 −0.023824−0.078216 −0.080886 +0.993650 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+664.004 +42.088 +196.822 +0.522858 +0.845297 +0.109967 −0.850267+0.526342 −0.003141 −0.060535 −0.091859 +0.993930 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +662.496 +39.920 +220.331 +0.522857 +0.845298+0.109967 −0.848824 +0.528138 −0.023831 −0.078222 −0.080882 +0.993650+0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +659.212 +37.781 +252.587+0.522857 +0.845298 +0.109966 −0.846183 +0.530272 −0.052783 −0.102930−0.065454 +0.992533 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +655.181+34.221 +298.538 +0.522860 +0.845296 +0.109966 −0.840531 +0.532730−0.098518 −0.141859 −0.040919 +0.989041 +0.000 +0.000 +0.000 +0.000150.00 0.00 0 +681.647 +78.923 +304.169 +0.522862 +0.845294 +0.109965−0.835756 +0.533740 −0.128969 −0.167709 −0.024471 +0.985533 +0.000+0.000 +0.000 +0.000 150.00 0.00 0 +685.540 +82.569 +258.259 +0.522857+0.845297 +0.109967 −0.842200 +0.532189 −0.086456 −0.131604 −0.047410+0.990168 +0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +689.865 +84.128+226.082 +0.522858 +0.845297 +0.109967 −0.845346 +0.530771 −0.060601−0.109594 −0.061274 +0.992086 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+692.342 +85.656 +202.600 +0.522858 +0.845297 +0.109967 −0.847222+0.529552 −0.042299 −0.093989 −0.071050 +0.993035 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +689.855 +84.094 +226.078 +0.522858 +0.845297+0.109966 −0.845347 +0.530770 −0.060585 −0.109580 −0.061282 +0.992087+0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +685.523 +82.527 +258.254+0.522859 +0.845296 +0.109966 −0.842202 +0.532189 −0.086433 −0.131584−0.047421 +0.990170 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +681.637+78.904 +304.166 +0.522864 +0.845293 +0.109964 −0.835757 +0.533741−0.128957 −0.167699 −0.024476 +0.985534 +0.000 +0.000 +0.000 +0.000150.00 0.00 0 STEP: 10 ROBO REFERENCE: ˜1977 +714.867 +163.941 +285.581+0.285202 +0.833560 −0.473115 −0.955565 +0.208895 −0.207988 −0.074539+0.511411 +0.856098 +0.000 +0.000 +0.000 +0.000 300.00 0.00 0 +709.551+142.956 +244.985 +0.285260 +0.833557 −0.473084 −0.958177 +0.236228−0.161537 −0.022895 +0.499379 +0.866081 +0.000 +0.000 +0.000 +0.00075.00 0.00 1 +710.325 +126.669 +216.866 +0.285292 +0.833547 −0.473084−0.958419 +0.251465 −0.134905 +0.006514 +0.491900 +0.870627 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +710.506 +114.917 +196.256 +0.285290+0.833546 −0.473086 −0.958047 +0.262173 −0.115809 +0.027498 +0.486278+0.873372 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +710.288 +126.625+216.894 +0.285265 +0.833552 −0.473091 −0.958427 +0.251449 −0.134877+0.006532 +0.491899 +0.870628 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0+709.512 +142.817 +245.064 +0.285269 +0.833549 −0.473093 −0.958174+0.236241 −0.161531 −0.022880 +0.499385 +0.866078 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +714.941 +163.913 +285.594 +0.285295 +0.833540−0.473094 −0.955534 +0.208956 −0.208069 −0.074578 +0.511419 +0.856089+0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +729.600 +207.416 +260.892+0.285209 +0.833562 −0.473107 −0.955212 +0.206563 −0.211901 −0.078906+0.512353 +0.855142 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +724.247+186.405 +220.312 +0.285280 +0.833552 −0.473081 −0.957984 +0.232693−0.167692 −0.029697 +0.501043 +0.864913 +0.000 +0.000 +0.000 +0.00075.00 0.00 1 +725.178 +170.058 +192.239 +0.285297 +0.833545 −0.473083−0.958437 +0.247065 −0.142680 −0.002048 +0.494126 +0.869388 +0.000+0.000 +0.000 +0.000 75.00 0.00 0 +725.662 +158.230 +171.664 +0.285293+0.833546 −0.473085 −0.958281 +0.257079 −0.124931 +0.017485 +0.488991+0.872114 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +725.134 +170.015+192.268 +0.285261 +0.833553 −0.473092 −0.958448 +0.247044 −0.142642−0.002025 +0.494124 +0.869389 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0+724.188 +186.283 +220.383 +0.285260 +0.833551 −0.473095 −0.957991+0.232692 −0.167653 −0.029662 +0.501046 +0.864912 +0.000 +0.000 +0.000+0.000 75.00 0.00 0 +729.633 +207.348 +260.929 +0.285273 +0.833545−0.473098 −0.955192 +0.206610 −0.211946 −0.078919 +0.512362 +0.855136+0.000 +0.000 +0.000 +0.000 150.00 0.00 0 STEP: 11 ROBO REFERENCE: ˜1977+707.521 +222.145 +254.718 −0.773933 +0.624241 +0.106537 −0.632835−0.756166 −0.166534 −0.023398 −0.196307 +0.980263 +0.000 +0.000 +0.000+0.000 300.00 0.00 0 +704.669 +226.234 +208.820 −0.773938 +0.624237+0.106529 −0.633253 −0.763762 −0.125134 +0.003250 −0.164306 +0.986404+0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +704.568 +231.609 +176.763−0.773937 +0.624237 +0.106531 −0.632985 −0.767553 −0.100961 +0.018744−0.145570 +0.989170 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +704.155+235.148 +153.360 −0.773937 +0.624238 +0.106531 −0.632567 −0.769950−0.083875 +0.029666 −0.132302 +0.990765 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +704.534 +231.627 +176.768 −0.773936 +0.624239 +0.106532−0.632986 −0.767555 −0.100936 +0.018761 −0.145552 +0.989173 +0.000+0.000 +0.000 +0.000 75.00 1.00 0 +704.579 +226.287 +208.831 −0.773936+0.624239 +0.106533 −0.633256 −0.763769 −0.125074 +0.003291 −0.164262+0.986411 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +707.527 +222.162+254.719 −0.773935 +0.624239 +0.106536 −0.632832 −0.756165 −0.166547−0.023406 −0.196316 +0.980261 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0+598.399 +312.233 +270.111 −0.773937 +0.624238 +0.106531 −0.633216−0.764900 −0.118175 +0.007716 −0.158918 +0.987262 +0.000 +0.000 +0.000+0.000 150.00 0.00 0 +595.625 +316.570 +224.168 −0.773937 +0.624238+0.106531 −0.632082 −0.771753 −0.069779 +0.038657 −0.121342 +0.991858+0.000 +0.000 +0.000 +0.000 75.00 0.00 1 +594.298 +320.494 +191.941−0.773937 +0.624238 +0.106532 −0.630603 −0.775106 −0.039386 +0.057987−0.097661 +0.993529 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +592.698+322.505 +168.425 −0.773937 +0.624238 +0.106532 −0.629164 −0.777078−0.017377 +0.071936 −0.080474 +0.994157 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +594.288 +320.503 +191.942 −0.773937 +0.624238 +0.106532−0.630602 −0.775106 −0.039380 +0.057991 −0.097657 +0.993529 +0.000+0.000 +0.000 +0.000 75.00 1.00 0 +595.595 +316.594 +224.172 −0.773937+0.624238 +0.106532 −0.632082 −0.771755 −0.069766 +0.038666 −0.121331+0.991859 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +598.369 +312.253+270.115 −0.773936 +0.624238 +0.106533 −0.633216 −0.764902 −0.118162+0.007726 −0.158908 +0.987263 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0STEP: 12 ROBO REFERENCE: ˜1977 +559.982 +343.786 +275.486 −0.773938+0.624236 +0.106531 −0.633056 −0.766940 −0.105080 +0.016108 −0.148766+0.988741 +0.000 +0.000 +0.000 +0.000 150.00 0.00 0 +555.669 +351.734+197.257 −0.773936 +0.624239 +0.106532 −0.629519 −0.776663 −0.022384+0.068766 −0.084388 +0.994057 +0.000 +0.000 +0.000 +0.000 75.00 0.00 0+594.223 +320.575 +191.951 −0.773939 +0.624235 +0.106532 −0.630598−0.775111 −0.039360 +0.058004 −0.097641 +0.993530 +0.000 +0.000 +0.000+0.000 75.00 0.50 1 +604.088 +312.595 +190.593 −0.773937 +0.624238+0.106532 −0.630874 −0.774627 −0.044169 +0.054950 −0.101393 +0.993328+0.000 +0.000 +0.000 +0.000 75.00 0.00 0 +594.326 +320.472 +191.937−0.773937 +0.624238 +0.106532 −0.630603 −0.775105 −0.039398 +0.057979−0.097671 +0.993528 +0.000 +0.000 +0.000 +0.000 75.00 1.00 0 +555.793+351.614 +197.240 −0.773934 +0.624242 +0.106532 −0.629525 −0.776657−0.022422 +0.068742 −0.084417 +0.994056 +0.000 +0.000 +0.000 +0.00075.00 0.00 0 +559.948 +343.798 +275.489 −0.773937 +0.624238 +0.106532−0.633058 −0.766942 −0.105058 +0.016123 −0.148749 +0.988743 +0.000+0.000 +0.000 +0.000 150.00 0.50 0

Although the above-disclosed embodiments have shown, described, andpointed out the fundamental novel features of the inventions as appliedto the above-disclosed embodiments, it should be understood that variousomissions, substitutions, and changes in the form of the detail of thedevices, systems, and/or methods shown may be made by those skilled inthe art without departing from the scope of the invention. Consequently,the scope of the inventions should not be limited to the foregoingdescription, but should be defined by the claims, where claim languagecarries an ordinary meaning as in customary usage and not by specialdefinition unless specifically stated as providing a definition.

1. A system for providing support for an object to be measured by anarticulator, comprising: a definition data; and a controller configuredso as to determine one or more support locations for said object basedon said definition data.
 2. The system of claim 1, wherein said one ormore support locations are determined based on determination of aselected desired orientation and position of said object.
 3. The systemof claim 2, wherein said orientation and position are determined basedon a selected preferred range of motion for said articulator.
 4. Thesystem of claim 1, further comprising one or more support members thatcan be moved to said support locations to provide said support for saidobject.
 5. The system of claim 4, wherein said one or more supportmembers are moved by said articulator based on known starting locationsof said one or more support members and said one or more supportlocations.
 6. The system of claim 4, wherein said one or more supportmembers are moved manually to said one or more support locations, saidmovements facilitated by said articulator being positioned at said oneor more support locations.
 7. The system of claim 4, wherein each ofsaid one or more support members comprises a base that allows lateralmovement or said support member, and a retractable member that providesadjustable height for the support location corresponding to said supportmember.
 8. The system of claim 7, wherein said retractable membercomprises a retractable tape.
 9. The system of claim 7, wherein saidsupport member further comprises a blocking member that inhibitsdownward movement of said retractable member.
 10. The system of claim 9,wherein said blocking member is actuated by said articulator.
 11. Thesystem of claim 7, wherein said support member further comprises astability enhancing member that selectively provides additionalstability of said support member.
 12. The system of claim 7, furthercomprising a return facilitating member disposed on said support memberand a nesting assembly configured to receive said return facilitatingmember.
 13. The system of claim 1, wherein said controller is furtherconfigured so as to obtain measurements of said object by movements ofsaid articulator, said articulator movements based on said definitiondata.
 14. The system of claim 13, wherein said controller is furtherconfigured so as to compare said object measurements with saiddefinition data.
 15. The system of claim 14, wherein said controller isfurther configured so as to perform a post-comparison operation.
 16. Thesystem of claim 15, wherein said post-comparison operation comprisesidentifying of differences between said object measurements and saiddefinition data.
 17. The system of claim 15, wherein saidpost-comparison operation comprises marking of said object based on saidcomparison.
 18. The system of claim 13, wherein said controller isfurther configured so as to adjust said articulator movements to accountfor deviations of said object from said definition data.
 19. A methodfor providing support for an object to be measured by an articulator,comprising: obtaining a definition data; and determining one or moresupport locations for said object based on said definition data.
 20. Themethod of claim 19, wherein said one or more support locations aredetermined based on determination of a selected desired orientation andposition of said object.
 21. The method of claim 20, wherein saidorientation and position are determined based on a selected preferredrange of motion for said articulator.
 22. The method of claim 19,further comprising generating signals for said articulator, said signalsresulting in movements of one or more support members to said supportlocations to provide said support for said object.
 23. The method ofclaim 22, wherein said one or more support members are moved by saidarticulator based on known starting locations of said one or moresupport members and said one or more support locations.
 24. The methodof claim 22, wherein said one or more support members are moved manuallyto said one or more support locations, said movements facilitated bysaid articulator being positioned at said one or more support locations.25. The method of claim 19, further comprising obtaining measurements ofsaid object by movements of said articulator, said articulator movementsbased on said definition data.
 26. The method of claim 25, furthercomprising comparing said object measurements with said definition data.27. The method of claim 26, further comprising performing apost-comparison operation.
 28. The method of claim 27, wherein saidpost-comparison operation comprises identifying differences between saidobject measurements and said definition data.
 29. The method of claim27, wherein said post-comparison operation comprises marking said objectbased on said comparison.
 30. The method of claim 25, further comprisingadjusting said articulator movements to account for deviations of saidobject from said definition data.
 31. A system for operating anarticulator, comprising: means for obtaining definition data; and meansfor determining one or more support locations for an object to bemeasured by said articulator based on said definition data.